The proposed model consists of two recurrent critics. The first critic adds a direct supervisory signal on the set of SMPL parameters \(s\in R^{k\cdot 85}\)  where \(k\)  is the set size (number of person shapes). It has an encoder network \((Enc(.))\)  for encoding the input which is a concatenation of a pair of the SMPL parameters set \(s\)  and text embedding \(x\) . It additionally has a recurrent fully connected LSTM network whose input in every iteration is a the encoded pair \(Enc(s_t)\)  corresponding to the SMPL parameters of one person \(s_t\)  generated in iteration \(t\) , and the text embedding \(x\) . The LSTM is iterated \(k\)  times where \(k\)  is the number of persons appearing in the image. Given the SMPL parameters alone which are simply represented as a real-valued vector, it is hard to distinguish whether a generated shape of the SMPL parameters ultimately corresponds to a realistic human shape or not and the network cannot learn the SMPL function which is responsible for generating the 3D body representation implicitly. Accordingly, in order to simplify the generator's task, we add an additional critic whose input is the rendered SMPL UV map images. These maps are downsampled using several convolutional layers and then each map's features are separately concatenated with the text embeddings and fed to the recurrent part of the critic. The rendered map is obtained from the set of vertices \(V\)  using a differentiable renderer that projects them onto the \(2D\)  space. This makes it possible to backpropagate through this part of the network as well, thereby making the entire pipeline differentiable. The advantage of these two critics is shown in the ablative studies such that when dropping either of them, the model fails to learn.
Based on WGAN's earth mover's distance, the critic's objective is to maximize the distance between the true and generated samples. This is reflected in the first term in eq. REF . Additionally, the critic should be able to discern when a pair of a SMPL set and text embeddings is real but is mismatched. This is reflected in the second term of eq. REF . WGAN's objective requires the critic to be Lipschitz continuous, which is guaranteed when the critic's gradient norm is constrained to 1 [1]}. The Lipschitz penalty term corresponds to the third term in eq.REF  and its term is expressed in eq. REF .
\(\begin{aligned}L_{D_{1}} = &-\mathbb {E}_{(s,x)\sim \mathbb {P}_r,z\sim \mathbb {P}_{z}}[D(s,x)-D(G(z,x),x)]\\& -\mathbb {E}_{(s,x)\sim \mathbb {P}_r,\bar{x}\sim \mathbb {P}_{x}}[D(s,x)-D(s,\bar{x})]\\& +\lambda L_{LP},\end{aligned}\) 
